Question: Complete the recursive formula of the geometric sequence $7\,,-14\,,\,28\,,-56,...$. $a(1)=$
Solution: The first term is $7$ and the common ratio is $-2$. ${\times (-2)\,\curvearrowright}$ ${\times (-2)\,\curvearrowright}$ ${\times (-2)\,\curvearrowright}$ $7,$ $-14,$ $28,$ $-56,...$ This is the recursive formula of $7\,,-14\,,\,28\,,-56,...$. $\begin{cases} a(1)=7 \\\\ a(n)=a(n-1)\cdot(-2) \end{cases}$